Almost all x-ray imaging systems use x-ray sources in which x-rays are generated when a beam of accelerated electrons impinges upon a target. The kinetic energy of the electrons is mostly converted to heat and only a small fraction to x-rays (referred to, in this context, as bremsstrahlung). Driven by the requirements of spatial resolution in imaging systems, x-ray tubes are designed to focus the electron beam onto a small area on the target. This area is commonly referred to as the tube's focal spot.
Definitions: As used herein, and in any appended claims, the term “x-ray tube” shall refer to any device in which electrons, or any other charged particles, are accelerated toward a target where they generate bremsstrahlung with photons having energies of at least 100 eV.
An x-ray target shall refer to any metal substrate impinged upon by energetic charged particles, for the generation of bremsstrahlung.
The term “x-ray source” shall signify a device that produces x-rays, including, without limitation, x-ray tubes, or bremsstrahlung targets impinged upon by energetic particles, without regard for the mechanism used for acceleration of the particles, including, without limitation, linacs, etc.
As the term is used herein, “focal spot” shall refer to a region on a target of an x-ray source impinged upon by energetic particles at a specified instant of time. Thus, focal spot is a dynamic concept in that it may be made to vary as a function of time.
The term “apparent focal spot” shall mean a projection of the focal spot onto a plane transverse to a direction (referred to herein as the “direction of x-ray extraction”) in which an x-ray beam is extracted from the x-ray tube.
As applied herein to a field of view (the cumulative angular extent encompassed by a scanning system), the term “large” shall denote that x-rays are extracted over an angular range larger than 30° to either side of a fiducial central direction.
Focusing electron beam power onto a region of a target which is too small may over-heat the target, resulting in the requirement that the target be cooled. The focal spot size limit is given by the allowable areal power density, which is a design parameter of an x-ray target. In order to decrease the apparent size of the focal spot, and thus increase spatial resolution, the x-ray radiation is typically extracted at a relatively shallow angle from the target surface. Common target angles (also known as “anode heel angles”), range from 20° down to 6°, thereby allowing the focal spot on the target to be about 3 to 10 times larger in area than the apparent focal spot, as defined above.
For a given target angle, the apparent focal spot size is optimized by elongating the actual focal spot on the target along the direction of x-ray extraction by a factor 1/sin(α) where α is the target angle. For imaging applications, the desired shape of the apparent focal spot is typically a square or a circle. A square shape is achieved by creating a rectangular actual focal spot with a side ratio of 1: sin(α), and the long dimensions aligned with the direction of x-ray extraction. A circular shape is achieved by creating an ellipse with an axes ratio of 1: sin(α) and the major axis along the direction of the x-ray extraction.
As long as the x-rays are extracted only in one fixed direction, the described prior-art approach works very well. However, imaging systems require the x-ray source to irradiate not only a single direction but a specified field of view, which is typically achieved in one of three principal ways: by using a cone beam, a fan beam, or a pencil beam.
In cone beam systems, a relatively large collimator opening creates the cone beam which irradiates the entire field of view at once. The typically rectangular field of view is spanned by two angles. Typically the smaller of these angles is limited by the target surface on one side (heel effect) and by an increasing apparent focal spot size on the other. The other (orthogonal) angle provides the desired aspect ratio. Both angles typically span less than ±30° and the distortion of the apparent focal spot for off-center angles is limited. Adjustable focal spots have been developed for this type of system allowing focal spot optimization for different fields of view and different beam power requirements. In U.S. Pat. No. 5,822,395, Schardt et al. propose electromagnetically shaping the cross-section of the electron beam to minimize the apparent focal spot distortions for off-center angles for selectable target angles and beam power levels. The shape and size of the focal spot remain fixed during image acquisition.
Fan beam systems cover their field of view by the fan beam opening angle in one dimension and by relative motion in the other. The image is acquired one line at the time. The fan beam is typically created normal to the impinging electron beam and the fan opening angles are often wider than for cone beam systems and can exceed ±45°. The apparent focal spot can be fully optimized only for one extraction angle, normally the center of the fan beam. With increasing off-center angle the apparent focal spot becomes distorted.
Pencil beam systems acquire the image data sequentially, pixel by pixel. The pencil beam scans the imaging object in two dimensions. Most pencil beam systems cover one dimension by relative motion and the other by moving an aperture in front of a stationary x-ray tube. Accordingly, the apparent focal spot suffers the same distortion as for the fan beam system.
Angles associated with bremsstrahlung targets are now described with reference to prior art practice and the resultant beam distortion.
FIG. 1 shows a prior art stationary x-ray tube target 10. The actual focal spot 12 is outlined by the dotted line ellipse 11. Focal spot 12 is the cross-section of an electron beam 16 generated at cathode 17 and impinging on the target 10 from above. Target angle α in the illustration of FIG. 1 is 20°. The angle φ spans the fan beam or the scan angle range of the pencil beam. The two arrows 13 and 14 indicate the directions of x-ray extraction for φ=0 (fan beam center) and φ=60°, respectively. In particular, arrow 14 serves only as one example for off-center extraction.
FIGS. 2A and 2B show the same prior art target 10 as shown in FIG. 1, with focal spot 12, but oriented so that the φ=0 (in FIG. 2A) and φ=60° (in FIG. 2B) direction are normal to the page. For φ=0 (in FIG. 2A), the apparent focal spot 20, as viewed from the direction of emitted beam propagation, has the desired circular shape. In the off-center view (FIG. 2B) the apparent focal spot deviates significantly from the ideal circular shape.
FIG. 3 identifies the three angles associated with the distortion of the apparent focal spot: the skew angle σ, the slant angle ε of the ellipse, and the slant angle δ of the diagonal. It should be noted, that all three angles are in the same plane, the image plane of FIG. 3.
FIG. 4 shows the distortion of the apparent focal spot at various angles φ for three target angles α. Starting with a square shaped apparent focal spot 40 for φ=0, the apparent focal spot will be skewed and compressed horizontally with increasing angle φ. The skew angle σ of parallelogram 42 is a function of the target angle α and the x-ray extraction angle φ:σ=arc tan[cot(α)sin(φ)]
The horizontal compression factor is simply cos(φ). Note, that the vertical extent remains unchanged. The lengths and slant of the long diagonal d of the parallelogram shaped apparent focal spot depends on the angles α and φ according to:d=√{square root over (1+(cos(φ)+cot(α) sin(φ))2)}
Slant angle δ is larger than the skew angle α:δ=arctan[cot(α) sin(φ)+cos(φ)].
The geometric transformation of the φ=0 apparent focal spot is given by the matrix m:
  m  =      (                                        cos            ⁡                          (              φ              )                                                                          cot              ⁡                              (                α                )                                      ⁢                          sin              ⁡                              (                φ                )                                                                          0                          1                      )  For φ>0 this transformation turns a circular apparent focal spot at φ=0 into an ellipse. The eccentricity of this ellipse increases with φ. Its axes and slant angle ε can be found through Singular Value Decomposition of the matrix m.
FIG. 5 shows how the skew angle σ, the slant angle δ of the diagonal, and the slant angle ε of the ellipse vary with the extraction angle φ in case of a 20° target angle α. The slant angles of the ellipse's major axis and the parallelogram's diagonal start from 45° at φ=0. The ellipse's slant angle is always smaller than that of the parallelogram's diagonal and both are always larger than the skew angle σ of the parallelogram.
The fact that the minor axis of an elliptical apparent focal spot shrinks as φ increases is not detrimental to imaging, but the growing major axis results in reduced spatial resolution. The same is true for the growing diagonal of a parallelogram shaped apparent focal spot.
An approach suggested by Safai et al. in U.S. Pat. No. 7,529,343 requires a rotating x-ray target. That approach may eliminate the distortion of the apparent focal spot, but only as long as the x-ray extraction angle remains aligned with the target and the electron beam cross section is not elongated. An elongated cross-section would result in a spinning apparent focal spot as the target rotates unless the electron-beam cross-section also co-rotates with the target. in which case rotating the entire tube would likely be the simpler implementation. Safai '343 provides no teaching of such a method.
If the electron beam cross-section is not elongated, only a 45° target angle creates a non-elongated apparent focal spot. In this case the actual focal spot is enlarged by merely a factor √{square root over (2)} which does not significantly alleviate the power density constraints. All this makes the solution proposed by Safai et al. complex, expensive to implement and inadequate for imaging applications requiring high power densities.
It would thus be advantageous to find a better way to compensate for distortion arising due to selecting target angles that vary over a large field of view, a way which preserves the advantages of small target angles and eschews the complexities of introducing moving parts inside the vacuum tube It would be furthermore advantageous to find a method to compensate for focal spot distortions which is applicable to scanning electron beam x-ray sources, such as for example described by Watanabe in U.S. Pat. No. 4,045,672.